Holden is trying to determine the velocity of his race car. He went 20 meters east, turned around, and went 40 meters west. He turned the car one more time and went 35 meters east. His car was 15 meters from the starting line. This took 5 seconds. What is the car’s velocity?

Final answer:

To find Neil's velocity relative to Barbara, their individual velocities are considered as vectors and subtracted. Neil's relative velocity is calculated to be approximately 6.74 m/s at 69° north of west.

Explanation:

To determine Neil's velocity relative to Barbara, we need to consider both Neil’s and Barbara's velocities as vectors and subtract the velocity of Barbara from Neil's velocity. Barbara is moving due south at 6.3 m/s, and Neil is moving due west at 2.4 m/s. By defining south as the negative y-direction and west as the negative x-direction, we can represent Barbara’s velocity vector as (0 m/s, -6.3 m/s) and Neil's as (-2.4 m/s, 0 m/s).

To find Neil’s velocity relative to Barbara, we calculate the vector difference: Neil’s velocity minus Barbara's velocity:

VNB = VN - VB = (-2.4 m/s, 0 m/s) - (0 m/s, -6.3 m/s) = (-2.4 m/s, 6.3 m/s)

To find the magnitude of Neil's relative velocity (VNB), we use the Pythagorean theorem: |VNB| = √((-2.4 [tex]m/s^2[/tex] + (6.3 [tex]m/s^2[/tex]), which gives:

|VNB| = √(5.76 + 39.69) = √(45.45) ≈ 6.74 m/s

The direction relative to due west can be found using the arctangent of the y-component over the x-component:

θ = arctan(6.3 / 2.4) ≈ arctan(2.625) ≈ 69°

Therefore, Neil's velocity relative to Barbara is approximately 6.74 m/s at an angle of 69° north of west.

Final answer:

The largest torque that can be applied to the solid aluminum shaft is 1.5 MPa.

Explanation:

To determine the largest torque that can be applied to the solid aluminum shaft, we need to consider the allowable shear stress and the diameter of the shaft. The formula to calculate torque is t = rF sin 0, where t is the torque, r is the radius, F is the applied force, and 0 is the angle between the force and the radius. In this case, since the force is perpendicular to the radius, the angle is 90 degrees, so sin 0 = 1.

The diameter of the shaft is given as 50mm, which means the radius is 25mm. We need to convert the radius to meters, so the radius is 25/1000 = 0.025m. The allowable shear stress is given as 60MPa.

Using the formula for torque, t = rF = (0.025m)(60MPa) = 1.5MPa.

Therefore, the largest torque that can be applied to the shaft is 1.5MPa.

The total work done by the donkey to pull the cart out of the mine is calculated by finding the work done against gravity and friction. The work done against gravity is 37012.5 J and against friction is 11637.5 J. The sum, and thus the total work done, is 48650 J.

To find the total work done by the donkey, we need to consider the work done against both the gravitational force and the frictional force. The total work done will be equal to the sum of these two works.

Firstly, let's find the work done against the gravitational force. The force of gravity acting on the cart can be found using the equation F = m x g x sin(θ), where m is the mass of the cart, g is the acceleration due to gravity, and θ is the angle of the slope. Therefore, F = 413 kg x 9.81 m/s² x sin(4.69°) = 211.5 N. The work done against gravity is then W = F x d, where d is the distance the cart is hauled, resulting in W = 211.5 N x 175 m = 37012.5 J.

Secondly, let's calculate the work done against friction. The frictional force can be found using the equation F = μ x m x g x cos(θ), where μ is the coefficient of friction. Therefore, F = 0.0163 x 413 kg x 9.81 m/s² x cos(4.69°) = 66.5 N. The work done against friction is again W = F x d, giving W = 66.5 N x 175 m = 11637.5 J.

The total work done by the donkey is then the sum of these two works, giving 37012.5 J + 11637.5 J = 48650 J.

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The electric flux through this area:

This is defined as the number of electric field lines that intersect a given area.

Electric flux(φ)= EA cos θ

where θ = angle between the directions of E and A is the surface area.

When the electric field is perpendicular to the surface,  θ = 0°.

φ = EA cos(0°)  = (6.20 x 10⁵ N/C)*(3.2 m²) × 1 = 1.984 x 10⁶ Nm²/C

When the electric field is parallel to the area, then θ = 90°, and

φ = EA cos(90°) = 0 as result of cos 90° being zero.

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Final answer:

The airplane's acceleration that caused the passenger to feel 170 N heavier is 2.33 m/s² upwards.

Explanation:

When a person experiences an increase in weight due to airplane turbulence, it indicates that there's an additional force acting on them because of the airplane's acceleration. To find the magnitude and direction of the airplane's acceleration, we can use Newton's second law of motion (F=ma), where F is the force, m is the mass, and a is the acceleration.

The student feels 170 N heavier, implying that the upward acceleration of the airplane is causing this additional force. Since the student's mass is 73 kg, we can calculate the acceleration using the formula a = F/m, where F is the additional force (170 N) and m is the mass of the student (73 kg). Hence, a = 170 N / 73 kg = 2.33 m/s². This is the magnitude of the acceleration.

The direction of the acceleration is upwards, as it increases the normal force which is felt as an increase in apparent weight.

The car's original speed can be calculated by utilizing the kinematic equation which is a principle in physics. Given that the car came to a stop with constant deceleration in a certain distance, the estimated initial speed was approximately 26.9 m/s.

The subject of the question involves concepts in physics specifically related to the equations of motion. To solve this, we can utilize the kinematic equation which relates initial velocity, acceleration, and distance: v2 = u2 + 2as, where 'v' is the final velocity, 'u' is the initial velocity, 'a' is acceleration and 's' is distance. Since the car comes to a stop, our final velocity v = 0 m/s. We know that the distance s = 30m and the acceleration is given as a = -3.50 m/s2 (negative because it's deceleration). From these, we can find the initial velocity 'u'. When we substitute these values into the equation, we can solve for 'u' as √(v2 - 2as), which equals approximately √(0 - 2*-3.50*30) ≈ 26.9 m/s. Therefore, the car's original speed was approximately 26.9 m/s.

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Final answer:

Large bodies of water like oceans contribute to more moderate climates in coastal areas due to their thermal properties. Global warming is leading to sea level rise through glacial meltwater and thermal expansion, which affects coastal communities. Oceans also impact global weather patterns, including precipitation and climate, due to heat transport and storage.

Explanation:

Large bodies of water, like oceans and large lakes, have a significant impact on the climate of coastal communities. The thermal properties of water, which heats and cools more slowly than land, lead to moderate climates in coastal areas. These regions typically experience smaller temperature fluctuations both daily and seasonally, in comparison to interior landmasses. Additionally, global warming is causing sea levels to rise due to glacial meltwater and thermal expansion, further complicating the climate effects on coastal communities. The warmth of oceanic currents is transported across vast distances, affecting the weather patterns far inland as well.

As the planet warms, the rise in sea levels can lead to the inundation of shorelines, which poses challenges for coastal cities. This rising sea level can increase the impact of storm surges, putting infrastructure at risk. The warming of oceans also contributes to the continued melting of polar ice, which can disrupt the supply of freshwater and bring about long-term changes to global precipitation and climate patterns. Hence, the oceans play a crucial role in moderating global climate and the long-term implications of climate change.

The horizontal force would be necessary to displace its position 0.16 m to one side will be 10.7 N.

Horizontal force is defined as a force applied in a direction parallel to the horizon. A force exerted on a body has two components: a horizontal component and a vertical component.

Given that,

m = 30 kg,

W = mg = (30 kg)*(9.8 m/s²)

W = 294 N, the weight of the chandelier.

Let T = tension in the wire.

Let F = the horizontal force required to displace the chandelier by 0.16 m.

The angle that the wire makes with the vertical is given by:

sin(θ) = 0.16/4.4 = 0.0364

θ = sin⁻¹ 0.0364

θ = 2.084°

For equilibrium,

T cos(θ) = W

0.9993T = 294

T = 294.195 N

We know that,

F = Tsin(θ)

F = 294.195*0.0364

F = 10.709 N

Thus, The horizontal force would be necessary to displace its position 0.16 m to one side will be 10.7 N.

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Answer:B,C, They cannot tell the difference between people and other objects. & They will wait for crossing pedestrians even if signaled to keep driving.

Explanation: i just did it on edg

Driverless cars can disrupt traffic due to slow speeds and over-caution, struggle to differentiate between people and objects, unexpectedly move to avoid hazards, and may not allow human control in emergency situations.

Driverless cars, or autonomous vehicles, have several disadvantages that might affect their performance and usability. Firstly, these vehicles often operate at safer, slower speeds than typical road traffic, which can disrupt normal traffic flow. Secondly, while they use advanced sensors to detect their surroundings, they might struggle to differentiate between people and other objects. This could potentially lead to harmful incidents. Additionally, they might be overly cautious and halt for crossing pedestrians even when it's unnecessary, causing further disruption.

Moreover, unpredictable actions like veering off the road to circumvent hazards could pose risks to passengers or other vehicles. Lastly, a key issue is if these vehicles don't permit the human driver to override control manually in crisis situations, which can decrease the human's ability to avert dangerous situations.

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Answer:

Acceleration is the rate of change in velocity.

Explanation:

Velocity,v-

"It is the change in a body's displacement or change in speed,d over the time,t."

Acceleration,a-

"When the body has a varying velocity,v across a given time frame,t is called as the acceleration,a."

Final answer:

The roller coaster's speed at the top of the loop is calculated using the centripetal acceleration formula, with the given downward acceleration of 1.50 g which equals 14.7 m/s² and the radius of curvature of 11.0 m to find the velocity.

Explanation:

The speed of the roller coaster at the top of the loop can be determined by utilizing the concept of centripetal acceleration. Centripetal acceleration is provided by the gravitational force when the roller coaster is at the top of the loop. Given that the downward acceleration is 1.50 g, and knowing that 1 g equals 9.8 m/s2, we can calculate the centripetal acceleration as 1.50 times 9.8 m/s2. The formula for centripetal acceleration (ac) is ac = v²/r, where v is the velocity and r is the radius of curvature. Rearranging the formula to solve for v gives us v = √(ac × r). Plugging in the values, we have v = √((1.50 × 9.8 m/s2) × 11.0 m), which yields the speed of the roller coaster at the top of the loop.

Solution, colloids and suspension are distinctive sort of mixtures.

Air and dust are not solutions.

There is an uncertainty about whether air and dust form a colloid or a suspension.

Colloids don't partitioned, while suspension's segments do isolated. In the event that the residue is sufficiently little it will stay in air sufficiently long to be considered  a colloid for all efects.

At that point, the most satisfactory assessment is that the  blend of air and dust is a colloid.

So, option c. a colloid is the answer.

Colloid is a heterogeneous mixture in which molecule estimate is middle of genuine arrangement and suspension. Smoke from a fire is case of colloidal framework in which small particles of strong buoy in air. Some basic cases of colloids are jewel stones, smoke, cheddar, drain, cleanser foam and froth.

The direction of the centripetal force when applied to an object is perpendicular to the object's motion.

Any motion along a curved road is accelerated, necessitating the application of force to the path's center of curvature. This force is known as the centripetal force, which is a force that seeks its center.

The direction of centripetal force, or even net force, is always that of acceleration. As an illustration, consider how quickly the earth is moving toward the sun. We are not moving toward the sun since the acceleration vector for planet Earth is constantly pointing in that direction and the velocity is perpendicular to it.

When force applied to an item, the centripetal force's direction is perpendicular to the object's motion.

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The pressure at the stagnation point is 149.854 lb/ft².

According to Bernoulli's equation, the total pressure at a given point is the sum of the static pressure and the dynamic pressure. The dynamic pressure is given by 0.5 * ρ * v^2, where ρ is the density of the fluid and v is the velocity of the fluid. In this case, the static pressure is -2.0 psi (a vacuum) and the velocity is 150 ft/s. The density of air at sea level is approximately 1.14 kg/m³, which is equivalent to 0.075 lb/ft³. Converting the units, we have -2.0 psi = -18.896 lb/ft². Plugging in the values into Bernoulli's equation, we can calculate the dynamic pressure:

Dynamic pressure = 0.5 * (0.075 lb/ft³) * (150 ft/s)^2 = 168.75 lb/ft².

The total pressure at the stagnation point is equal to the sum of the static pressure and the dynamic pressure. Therefore, the pressure at the stagnation point is:

Total pressure = -18.896 lb/ft² + 168.75 lb/ft² = 149.854 lb/ft².

The most reactive element of this list is Chlorine, the next most reactive is bromine, and the least reactive is iodine.

All of these three elements are group 7 elements in the periodic table. It is known that the reactivity of group 7 elements decreases down the group. The most reactive element in this group is Flourine  with reactivity decreasing down the group.

The reason for this decrease in reactivity is that as you go down the group, the distance between the positive nucleus that attracts valence electrons increases, decreasing the electrostatic attraction between the nucleus and the outer electrons. The other reason is that the electrons in lower energy levels closer to the nucleus repel and shield the electrons in the outermost shell or energy level of the atom.

Chlorine>Bromine>Iodine.

Answer: The order of reactivity of non-metals from most reactive to least reactive is [tex]\text{Chlorine}>\text{Bromine}>\text{Iodine}[/tex]

Explanation:

Reactivity of a non-metal is defined as the tendency of an element to gain electrons. The reactivity increases as we move across a period and it  decreases as we move down the group.

When the size of an element increases, the valence electrons gets away from the nucleus and the tendency of an element to gain electrons decreases.

In a group, the size of an element increases because there is an addition of new shell and electron is added in that shell.

The given elements belong to the same group which is Group 17.

Chlorine has the smallest size, then bromine and then iodine.

Hence, the order of reactivity of non-metals from most reactive to least reactive is [tex]\text{Chlorine}>\text{Bromine}>\text{Iodine}[/tex]

Without the given Figure, precise answers can't be provided. Generally, acceleration is calculated as the slope of the velocity-time graph, and position is provided by the integral (or area under the graph) of the velocity-time graph. The object's speed is lowest when its velocity is minimal, and it is farthest from x= 0 when the accumulated area under the graph is maximum.

Unfortunately, without the given Figure P2.50, it's impossible to accurately calculate the object's acceleration, position at different times, or specify when the object is moving with the lowest speed or is farthest from x = 0.

However, I can explain the general method to determine this information. Acceleration is calculated from the slope of the velocity-time graph. The position is generally obtained by calculating the area under the velocity-time graph from the beginning of the interval to the end. The object is moving with the lowest speed when the velocity is lowest (either positively or negatively). The object is farthest from x = 0 when the accumulated area under the velocity-time graph (counting areas below the time axis as negative) is a maximum. The total distance the object has moved is equal to the absolute sum of all the areas (both positive and negative) on the velocity-time graph.

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The correct answer would be letter d, 8.3.

Solution for the problem follows:

Given are:

B = 6i - 8j 

A is unknown; let A be = mi + nj 

A+B is along the x axis (therefore A+B = Ki + 0j, where K is unknown,

but then again the magnitude of A+B is the similar as the magnitude of A,

so mag(A+B)=K=sqrt(m^2+n^2), or K^2 = m^2+n^2. 

A+B, from simple vector addition, will be now (m+6)i + (n-8)j.

Ever since we previously know A+B = Ki + 0j, we now know that: 

m+6 = K 

n-8 = 0, which implies n=8. 

Thus, K^2=m^2+n^2 ====> (m+6)^2 = m^2 +8^2 

= m^2 + 12m + 36 = m^2 + 64 

= 12m = 28 

= m = 2.33333... 

Therefore, the magnitude of A is sqrt[(2.333...)^2 + 8^2] = 8.3333

The magnitude of [tex]\vec A[/tex] is [tex]8.3[/tex].

Further explanation:

A vector is a quantity having magnitude and direction both. It is represented as the product of magnitude and direction vector.

Given:

The vector is given as [tex]\vec B = 6\hat i - 8\hat j[/tex].

The direction of resultant vector is in the X- direction.

Concept used:

Consider a vector [tex]\vec A = a\hat i + b\hat j[/tex] which is added to [tex]\vec B[/tex] to get a resultant vector [tex]\vec C[/tex]. The resultant vector is directed in the positive X-direction which means that the y- component of the vector is zero.

The expression for the resultant vector is given as.

[tex]\vec C = \vec A + \vec B[/tex]

Substitute [tex]6\hat i - 8\hat j[/tex] for [tex]\vec B[/tex] in the above expression.

[tex]\begin{gathered}\vec C = \left( {a\hat i + b\hat j} \right) + \left( {6\hat i - 8\hat j} \right) \\= \left( {a + 6} \right)\hat i + \left( {b - 8} \right)\hat j \\ \end{gathered}[/tex]

The resultant vector is represented as.

[tex]\vec C = x\hat i + 0\hat j[/tex]

Compare the above two expression of resultant vector.

[tex]x = a + 6[/tex]                                         …… (1)

[tex]\begin{aligned}0&=b-8\\b&=8\\\end{aligned}[/tex] 

The magnitude of resultant vector is equal to the magnitude of [tex]\vec A[/tex].

The expression for the magnitude of [tex]\vec A[/tex] is given as.

[tex]\left| {\vec A} \right| = \sqrt {\left( {{a^2}} \right) + \left( {{b^2}} \right)}[/tex]                           …… (2)

The expression for the magnitude of [tex]\vec C[/tex] is given as.

[tex]\left| {\vec C} \right| = \sqrt {{{\left( {a + 6} \right)}^2}}[/tex]

Compare the above two expressions.

[tex]\sqrt {\left( {{a^2}} \right) + \left( {{b^2}} \right)}= \sqrt {{{\left( {a + 6} \right)}^2}}[/tex]

Substitute 8 for [tex]b[/tex]  in above expression.

[tex]\begin{aligned}\sqrt {\left( {{a^2}} \right) + \left( {{8^2}} \right)}&=\sqrt {{{\left( {a + 6} \right)}^2}}\\{a^2} + 64&={a^2} + 36 + 12a \\12a&=28 \\a&=2.33 \\ \end{aligned}[/tex]

Substitute 2.33 for a and 8 for b in equation (2).

[tex]\begin{aligned}\left| {\vec A} \right|&=\sqrt {{{\left( {2.33} \right)}^2} + {{\left( 8 \right)}^2}}\\&=8.33 \\ \end{aligned}[/tex]

Thus, the magnitude of vector A is [tex]8.33[/tex].

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Answer Details:

Grade: College

Subject: Physics

Chapter: Vectors

Keywords:

Vectors, product, magnitude, direction, resultant vector, adding vector, subtraction of vector, 2.33, 8, 8.33, 8.3, 8.33.

Final answer:

The question requires calculating the rate at which two individuals are moving apart by using their speeds and applying principles of kinematics. It involves converting time into seconds, calculating the total distance each person traveled, and then finding the distance between them 15 minutes after the woman starts walking.

Explanation:

The question involves calculating the rate at which two people are moving apart from each other, given their speeds and initial positions. It requires an understanding of relative motion and the ability to apply the principles of kinematics to solve real-world problems.

The man starts walking north from a point P at 2 ft/s, and five minutes later, a woman starts walking south from a point 500 ft due east of P at 6 ft/s. To find the rate at which they are moving apart 15 minutes after the woman starts walking, we must consider the distance each has traveled in their respective directions by that time.

The man walks for a total of 20 minutes (15 minutes after the woman starts), while the woman walks for 15 minutes. The distance the man walks is 2 ft/s × 1200 s = 2400 ft and the woman walks 6 ft/s × 900 s = 5400 ft. Since they start 500 ft apart east to west, and move in north-south directions, the distance between them after 15 minutes can be found using the Pythagorean theorem: √(24002 + (500 + 5400)2) = √(5760000 + 32400000) = √38160000, which gives the distance between them. The rate of separation is the derivative of this distance with respect to time, assuming constant speeds.

Answer: decomposers

Explanation: they are microorganisms that are responsible for the decay and break down of dead organism into nutrients that are available for the plant